4 papers
The average distance problem with perimeter-to-area ratio penalization
Qiang Du, Xin Yang Lu, Chong Wang
In this paper we consider the functional \begin{equation*} E_{p,\la}(Ω):=\int_Ω\dist^p(x,\pd Ω)\d x+\la \frac{\H^1(\pd Ω)}{\H^2(Ω)}. \end{equation*} Here , $\la>0$ are giv…
The average distance problem with an Euler elastica penalization
Qiang Du, Xin Yang Lu, Chong Wang
We consider the minimization of an average distance functional defined on a two-dimensional domain with an Euler elastica penalization associated with $\pd Ω$, the boundary of…
Minimizing optimal transport for functions with fixed-size nodal sets
Qiang Du, Amir Sagiv
Consider the class of zero-mean functions with fixed and norms and exactly nodal points. Which functions minimize , the Wasse…
On the convergence to local limit of nonlocal models with approximated interaction neighborhoods
Qiang Du, Hehu Xie, Xiaobo Yin
Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximat…